Barca won with a much-changed line-up thanks to goals from Fermin Lopez and Raphinha. The Catalans have the second-leg of their Champions League semifinal at Inter Milan later this week.
Afterwards, Flick said: "The goal is three points, and I'm happy to have gotten them. Mission accomplished.
"When there are a lot of changes, the automatisms are also different. I've been able to rest players.
"No. I'm not disappointed. When you make nine substitutions, it's not easy for the players; they're young. I believe in them. I have confidence. It wasn't easy.
"There were some mistakes, quick transitions, but Araujo and Christensen had a good game, and so did Ter Stegen."
Barca came from behind after Ivan Sanchez had Valladolid ahead on six minutes.
Flick added, "I don't like teams that say, 'That's it,' when they win 2-0. I'm very happy with the mentality and attitude we have."